Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model

Details Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model

2011-01-28

arxiv.org/abs/1101.5543v1

Mathematics

Dynamical Systems

33 pages, 5 figures

Scientific paper

We study the discretized version of a dynamical system given by a model proposed by Yoccoz and Birkeland to describe the evolution of the population of Microtus Epiroticus on Svalbard Islands, see ${\rm http://zipcodezoo.com/Animals/M/Microtus\_\,epiroticus}$. We prove that this discretized version has an attractor Lambda with a hyperbolic 2-periodic point p in it. For certain values of the parameters the system restricted to the attractor exhibits sensibility to initial conditions. Under certain assumptions that seems to be sustained by numerical simulations, the system is topologically mixing explaining some of the high oscillations observed in Nature. Moreover, we estimate its order-2 Kolmogorov entropy obtaining a positive value. Finally we give numerical evidence that there is a homoclinic point associated with p.

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